Here is the full list of all 21 Touhou Mystery Reel achievements.
Get the last hit of Reimu immediately after she falls
Perfectly counter Reimu's aerial attacks several times
Make the chicken soup
Defeat Reimu
Gain friendliness of the fortune cat
Clear Youmu's training
Completely defeat Motoori Kosuzu
Some things should not be done
Clear stage 1 and complete the mission
Defeating Motoori Kosuzu
Make Motoori Kosuzu step on the banana
Help little fairy
Complete Flandre's rehearsal
Complete Sakuya's challenge
Open the game at least once